sas task due today Case Solution
Data Description
The dataset provided the data for four different treatment with respect to the baseline weights of the subject along with the weight gained during trial and the feeding intake by the subject. The variable were represented as, TRTGRP, BLWEIGHT, WTGAIN and INTAKE respectively. The dataset was imported into the SAS software through Import PROC function to estimatesingle and two factor Anova model.
Creating New Binary Variable INTAKEGRP
INTAKEGRP | ||
TRTGRP | Group-1 | Group-2 |
1 | 2506.18 | |
1 | 2492.19 | |
1 | 2641.53 | |
1 | 2615.22 | |
1 | 2640.8 | |
1 | 2441.05 | |
1 | 2533.92 | |
1 | 2468.29 | |
2 | 2362.64 | |
2 | 2527.55 | |
2 | 2559.16 | |
2 | 2374.77 | |
2 | 2435.52 | |
2 | 2526.46 | |
2 | 2407.5 | |
2 | 2362.38 | |
3 | 2682.09 | |
3 | 2654.62 | |
3 | 2683.28 | |
3 | 2605.4 | |
3 | 2706 | |
3 | 2613.29 | |
3 | 2508.74 | |
3 | 2550.34 | |
4 | 2384 | |
4 | 2510.3 | |
4 | 2460.87 | |
4 | 2470.7 | |
4 | 2505.14 | |
4 | 2517.2 | |
4 | 2417.8 | |
4 | 2554.02 |
Single-Factor Anova
Using Single factor Anova function in SAS (PROC GLM) function to compare the different treatment groups. Through which, it can be determined that, mean value of weight gained by subject amounts to 1,415.42, calculated from the dataset provided. Whereas, the p-value of Single-factor Anova is significantly lower than the significance level at 0.05. Which means there is enough substantial evidence present to validate the null hypothesis that, the weigh gained by subjectdepends on the treatment groups. Therefore, the Null hypothesis can be accepted.
Anova: Single Factor (PROC GLM) | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
TRTGRP | 32 | 80 | 2.5 | 1.29 | ||
WTGAIN | 32 | 45,293.50 | 1,415.42 | 5,711.72 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 31,941,571.60 | 1.00 | 31,941,571.60 | 11,182.04 | 9.79E-72 | 4.00 |
Within Groups | 177,103.33 | 62.00 | 2,856.51 | |||
Total | 32,118,674.93 | 63.00 |
Two-way Anova
By conducting a two-way Anova in SAS to compare the Weight gains with independent variables available in the dataset. After first it was evaluated that, using TRTGRP and INTAKEGRP variables with their interactions, the two-way Anova’s P-value calculated was insignificant, as it was above the significant level at 0.05.Therefore, the above mentioned variables were used without their interaction to estimate the p-value under two-way Anova.Through which, it can be determined that, as the p value generated is significantly lower than the significance level at 0.05. Which mean that, there is substantial evidence present to validate the null hypothesis. In which, the null hypothesis estimated that, the weight gained by the subject where dependent on the types of treatment and their feeding intake by groups.
Anova: Two-Factor Without Replication | ||||||
SUMMARY | Count | Sum | Average | Variance | ||
INTAKE | 32 | 80,718.95 | 2,522.47 | 9,660.20 | ||
Group-1 | 32 | 41,625.27 | 1,300.79 | 1,542,726.41 | ||
Group-2 | 32 | 39,093.68 | 1,221.68 | 1,747,750.29 | ||
Two-Factor ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Rows | 399288 | 31 | 12880.26359 | 0.007836482 | 1 | 1.636151 |
Columns | 34035290 | 2 | 17017645.14 | 10.35370647 | 0.000132 | 3.145258 |
Error | 101904955 | 62 | 1643628.317 | |||
Total | 136339534 | 95 |
Covariance Analysis
By conducting a covariance analysis in SAS software to compare the weight gain with the intake and baseline weight.In which, all the variables were considered excluding INTAKEGRP (Group 1 & 2). Hence, it can be determined that, the covariance between Weight gain and Baseline weight amounts to a positive 1826, which was significantly higher than 0.08, the benchmark. Which mean that these two variables are highly correlated with one another and a small change in one of these variables would show a significant change in the other. Whereas, the covariance between weight gains and intake amounts to a negative 1789. Which meant that, the variables were inversely related, where a small increase in one variables would show a significant decrease in the other, attributed to their negative covariance value.
Covariance Analysis | ||||
TRTGRP | BLWEIGHT | WTGAIN | INTAKE | |
TRTGRP | 1.25 | |||
BLWEIGHT | -40.80359375 | 3328.565711 | ||
WTGAIN | -53.7359375 | 1826.975483 | 5533.229209 | |
INTAKE | -1.71359375 | 1240.1969 | -1789.467438 | 9358.316514 |
Treatment-1 Our Company’s Brand
Under the assumption that, Treatment-1 is our company’s brand, it can be determined that, the mean of Baseline weight of subjects engaging in treatment-1 was higher than the baseline weights of subjects engaging in other types of treatment. Similarly, the average weight gained by subjects in treatment-1 was more than the average weight gained by subject engaging its other types of treatments. Whereas, it was assessed that, the average feeding intake of each subject in the trial was more for other types of treatments then treatment-1.Therefore, it can be evaluated that, the subjects engaged in treatment-1 had higher average baseline weighs. Which, in turn, compelled them to register higher average weight gains by their subjects compared to other subject engaged in other types of treatments. Furthermore, the kurtosis of baseline weight, weight gained and intake in treatement-1 amounted to a negative value. Which meant that, the probability of next value generated in the distribution would be lower, was high and it would meet or reach its outliers less frequently. On the other hand, the kurtosis of Weight gains and intake for all other types of treatment amounted to a negative value as well. Whereas, the kurtosis for baseline weight for all other treatments amounted to a positive values. Which meant that, the probability of next value generated in the distribution would be higher, was high and it would meet or reach its outliers more frequently................................................................
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